Foliations of M 3 defined by ℝ 2 -actions

Jose Luis Arraut; Marcos Craizer

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 4, page 1091-1118
  • ISSN: 0373-0956

Abstract

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In this paper we give a geometric characterization of the 2-dimensional foliations on compact orientable 3-manifolds defined by a locally free smooth action of ℝ 2 .

How to cite

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Arraut, Jose Luis, and Craizer, Marcos. "Foliations of $M^3$ defined by ${\mathbb {R}}^2$-actions." Annales de l'institut Fourier 45.4 (1995): 1091-1118. <http://eudml.org/doc/75146>.

@article{Arraut1995,
abstract = {In this paper we give a geometric characterization of the 2-dimensional foliations on compact orientable 3-manifolds defined by a locally free smooth action of $\{\Bbb R\}^2$.},
author = {Arraut, Jose Luis, Craizer, Marcos},
journal = {Annales de l'institut Fourier},
keywords = {foliated manifolds; actions},
language = {eng},
number = {4},
pages = {1091-1118},
publisher = {Association des Annales de l'Institut Fourier},
title = {Foliations of $M^3$ defined by $\{\mathbb \{R\}\}^2$-actions},
url = {http://eudml.org/doc/75146},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Arraut, Jose Luis
AU - Craizer, Marcos
TI - Foliations of $M^3$ defined by ${\mathbb {R}}^2$-actions
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 4
SP - 1091
EP - 1118
AB - In this paper we give a geometric characterization of the 2-dimensional foliations on compact orientable 3-manifolds defined by a locally free smooth action of ${\Bbb R}^2$.
LA - eng
KW - foliated manifolds; actions
UR - http://eudml.org/doc/75146
ER -

References

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  1. [1]J.L. ARRAUT and M. CRAIZER, Stability of blocks of compact orbits of an action of ℝ2 on M3. Hamiltonian Systems and Celestial Mechanics., Edited by E.A. Lacomba and J. Libre, World Scientific (1993). Zbl0890.57052
  2. [2]J.L. ARRAUT and N.M. DOS SANTOS, Differentiable conjugation of actions of Rp, Bol. Soc. Bras. Mat., vol. 19, n.1 (1988), 1-19. Zbl0682.57011MR91e:58161
  3. [3]G. CHATELET and H. ROSENBERG, Un théorème de conjugaison des feuilletages, Ann. Inst. Fourier, Grenoble, 21-3 (1971), 95-106. Zbl0208.25703MR49 #11531
  4. [4]G. CHATELET, H. ROSENBERG and D. WEIL, A classification of the topological types of ℝ2-actions on closed orientable 3-manifolds, Publ. Math. IHES, 43 (1973), 261-272. Zbl0278.57015MR49 #11533
  5. [5]E. GHYS, T. TSUBOI, Différentiabilité des conjugaisons entre systèmes dynamiques de dimension 1, Ann. Inst. Fourier, Grenoble, 38-1 (1988), 215-244. Zbl0633.58018MR89i:58119
  6. [6]N. KOPPEL, Commuting diffeomorphisms. Global Analysis, Proc. of Symp. in Pure Math., AMS, XIV (1970). Zbl0225.57020
  7. [7]E.L. LIMA, Commuting Vector Fields on S3, Annals of Math., 81 (1965), 70-81. Zbl0137.17801MR30 #1517
  8. [8]R. MOUSSU, R. ROUSSARIE, Relations de conjugaison et de cobordisme entre certains feuilletages, Pub. Math. IHES, 43 (1973), 143-168. Zbl0356.57018MR50 #11269
  9. [9]H. ROSENBERG, R. ROUSSARIE and D. WEIL, A classification of closed orientable manifolds of rank two, Ann. of Math., 91 (1970), 449-464. Zbl0195.25404MR42 #5280
  10. [10]H. ROSENBERG and R. ROUSSARIE, Topological equivalence of Reeb foliations, Topology, vol. 9 (1970), 231-242. Zbl0211.26602MR41 #7712
  11. [11]N.C. SALDANHA, Stability of compact actions of Rn of codimension one, to appear in Comm. Math. Helvet. Zbl0841.57038
  12. [12]F. SERGERAERT, Feuilletages et difféomorphismes infiniment tangents à l'identité, Inventiones Math., 39 (1977), 253-275. Zbl0327.58004MR57 #13973
  13. [13]G. SZEKERES, Regular iteration of real and complex functions, Acta Math., 100 (1958), 163-195. Zbl0145.07903MR21 #5744
  14. [14]J.-C. YOCCOZ, Thesis. 
  15. [15]M. CRAIZER, Homogenization of codimension 1 actions of near a compact orbit, ℝn Ann. Inst. Fourier, Grenoble, 44-5 (1994), 1435-1448. Zbl0820.34021MR95m:58100

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